diff --git a/fuzzysearch/generic_search.py b/fuzzysearch/generic_search.py
index ad359bb..14b74fd 100644
--- a/fuzzysearch/generic_search.py
+++ b/fuzzysearch/generic_search.py
@@ -83,6 +83,16 @@ def find_near_matches_generic_linear_programming(subsequence, sequence,
                             subseq_index=cand.subseq_index + 1,
                             l_dist=cand.l_dist + 1,
                         ))
+                else:
+                    # cand.subseq_index == _subseq_len - 1
+                    if (
+                            cand.n_subs < max_substitutions or
+                            (
+                                cand.n_dels < max_deletions and
+                                cand.n_ins < max_insertions
+                            )
+                    ):
+                        yield Match(cand.start, index + 1, cand.l_dist + 1)
 
                 # try skipping subsequence chars
                 for n_skipped in xrange(1, min(max_deletions - cand.n_dels, max_l_dist - cand.l_dist) + 1):
diff --git a/tests/test_generic_search.py b/tests/test_generic_search.py
index 1869f2a..74d768a 100644
--- a/tests/test_generic_search.py
+++ b/tests/test_generic_search.py
@@ -3,6 +3,7 @@ from tests.test_levenshtein import TestFindNearMatchesLevenshteinBase
 from fuzzysearch.common import Match, get_best_match_in_group, group_matches
 from fuzzysearch.generic_search import \
     find_near_matches_generic_linear_programming as fnm_generic_lp
+from tests.test_substitutions_only import TestSubstitionsOnlyBase
 
 
 class TestGenericSearchAsLevenshtein(TestFindNearMatchesLevenshteinBase,
@@ -17,6 +18,14 @@ class TestGenericSearchAsLevenshtein(TestFindNearMatchesLevenshteinBase,
         ]
 
 
+class TestGenericSearchAsSubstitutionsOnly(TestSubstitionsOnlyBase,
+                                           unittest.TestCase):
+    def search(self, subsequence, sequence, max_subs):
+        return list(
+            fnm_generic_lp(subsequence, sequence, max_subs, 0, 0, max_subs)
+        )
+
+
 class TestGenericSearch(unittest.TestCase):
     def search(self, pattern, sequence, max_subs, max_ins, max_dels,
                max_l_dist=None):
diff --git a/tests/test_substitutions_only.py b/tests/test_substitutions_only.py
index 2163680..f59bc50 100644
--- a/tests/test_substitutions_only.py
+++ b/tests/test_substitutions_only.py
@@ -198,6 +198,11 @@ class TestSubstitionsOnlyBase(object):
              Match(start=99, end=109, dist=0)],
         )
 
+    def test_missing_at_beginning(self):
+        self.assertEqual(
+            self.search("ATTEST","TESTOSTERONE", max_subs=2),
+            [],
+        )
 
 class TestFindNearMatchesSubstitionsLinearProgramming(TestSubstitionsOnlyBase, unittest.TestCase):
     def search(self, subsequence, sequence, max_subs):